Finite Group DatabasebetaFinite Group Databasebeta| order | 4170 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊(D139⋊C3) |
| unambiguous semidirect product | (C139⋊C3)⋊D5 |
| unambiguous semidirect product | D695⋊C3 |
| Fitting, socle, derived, Hall | C5×C139 ⋊ C2×C3 |
| Hall | C5×C139⋊C3 ⋊ C2 |
| Hall | D695 ⋊ C3 |
| Hall | C139⋊C3 ⋊ D5 |
| Sylow | C139 ⋊ C3×D5 |
| Sylow | C5 ⋊ D139⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C139 | C2×C3 |
| LCS | G ▷ C5×C139 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 144 |
| transitive degree | μt(G) = 695 |
Polycyclic presentation:
2,3,5,139|c^a=c^4,d^a=d^138,d^b=d^96127 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4170, 12);